Is there any easy way by using windbg/ollydbg to figure out a memory range or simply an address is DEP-enabled or not?
For your case all "DEP enabled" for a process means is that the stack and heap are not writable and executable. By the time you can attach a debugger you just need to check if the stack and heap are ReadWrite or ReadWriteExecute.
In Windbg you can use either !vprot or !address to get this information. In Olly I believe there's a window under view that will give you a list of the memory regions in a process and their associated protections.
Additionally you can check the PE header of an executable to see if it supports DEP or not. The mona plugin gives you a quick command to see this, but there are probably others as well.